Normal Families of Meromorphic Functions and Shared Set

TIAN Hong-gen, CHEN Wei, YUAN Wen-jun

doi:10.13371/j.cnki.chin.q.j.m.2015.02.001

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 2: 159 - 165

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.02.001

Normal Families of Meromorphic Functions and Shared Set

Expand

1. School of Mathematics Science, Xinjiang Normal University 2. School of Mathematics and Information Science, Guangzhou University

TIAN Hong-gen(1957-), male, native of Hanjiang, Jiangsu, a professor of Xinjiang Normal University, engages in complex analysis; CHEN Wei(1988-), male, native of Ruichang, Jiangxi, a student of Xinjiang Normal University, M.S.D., engages in complex analysis and its applications; YUAN Wen-jun(1957-), male, native of Anyue, Sichuan, a professor of Guangzhou University, Ph.D., engages in complex analysis and its applications.

Received date: 2013-03-19

Online published: 2020-11-23

Supported by

Supported by the National Natural Science Foundation of China(11461070,11271090)； Supported by the Natural Science Foundation of Guangdong Province(S2012010010121)；

Fold

Abstract

In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers bf,c_fsatisfying（i） b_f/c_fis a constant;（ii） min{σ（0,b_f）,σ（0,c_f）,σ（b_f,c_f）} ≥m for some m > 0;（iii） E_f’（S_f）\subseteq E_f（S_f）,where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results of[10-11]and[7].

Key words： meromorphic function; shared set; normal family

Cite this article

TIAN Hong-gen, CHEN Wei, YUAN Wen-jun . Normal Families of Meromorphic Functions and Shared Set[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(2) : 159 -165 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.02.001

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article